Mann Iteration

Author

Eric W. Weisstein
January 24, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DynamicalSystems/MannIteration.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MannIteration.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

Mann[f_,x_,n_]:= Module[{v=x,i},
Table[
v=((i-1)v+f[v])/i,
{i,n}]
]

Examples

<<Utilities`Plot`

Plot[{Cos[x],x},{x,-2,2}]

IntegerListPlot[Mann[Cos,.2,100]]

FixedPoint[Cos,.2]

Plot[{Sech[x],x},{x,-2,2}]

IntegerListPlot[Mann[Sech,.2,100]]

FixedPoint[Sech,.2]